<h2>题目编号 : 270</h2>
<div style="color:#666;font-size:80%;">26 December 2009</div><br />
<div class="problem_content">
<p>A square piece of paper with integer dimensions N<img src='images/symbol_times.gif' width='9' height='9' alt='&times;' border='0' style='vertical-align:middle;' />N is placed with a corner at the origin and two of its sides along the <var>x</var>- and <var>y</var>-axes. Then, we cut it up respecting the following rules:
<ul>
<li>We only make straight cuts between two points lying on different sides of the square, and having integer coordinates.</li>
<li>Two cuts cannot cross, but several cuts can meet at the same border point.</li>
<li>Proceed until no more legal cuts can be made.</li>
</ul></p>

<p>Counting any reflections or rotations as distinct, we call C(N) the number of ways to cut an N<img src='images/symbol_times.gif' width='9' height='9' alt='&times;' border='0' style='vertical-align:middle;' />N square. For example, C(1)&thinsp;=&thinsp;2 and C(2)&thinsp;=&thinsp;30 (shown below).</p>
<div align='center'><img src="project/images/p_270_CutSquare.gif" /></div>

<p>What is C(30) mod 10<img src="" style="display:none;" alt="^(" /><sup>8</sup><img src="" style="display:none;" alt=")" /> ?</p>
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